Flux Observer

Compute electrical position, magnetic flux, and electrical torque of rotor

Library:
Motor Control Blockset / Sensorless Estimators

Description

The Flux Observer block computes the electrical position, magnetic flux, and electrical torque of a PMSM by using the per unit voltage and current values along the α- and β-axes in the stationary αβ reference frame.

Equations

These equations describe the computation of the electrical position, magnetic flux, and electrical torque by the block.

$ψ_{α} = \int^{} (V_{α} - I_{α} R) dt - (L \cdot I_{α})$

$ψ_{β} = \int^{} (V_{β} - I_{β} R) dt - (L \cdot I_{β})$

$ψ = \sqrt{ψ_{α}^{2} + ψ_{β}^{2}}$

$T_{e} = \frac{3}{2} P (ψ_{α} I_{β} - ψ_{β} I_{α})$

$θ_{e} = \tan^{- 1} \frac{ψ_{β}}{ψ_{α}}$

where:

$V_{α}$ and $V_{β}$ are the α-axis and β-axis voltages.
$I_{α}$ and $I_{β}$ are the α-axis and β-axis current.
$R$ is the stator resistance of the motor.
$L$ is the stator inductance of the motor.
$P$ is the number of motor pole pairs.
$ψ$ is the rotor magnetic flux.
$ψ_{α}$ and $ψ_{β}$ are the rotor magnetic fluxes along the α- and β-axes.
$T_{e}$ is the electrical torque of the rotor.
$θ_{e}$ is the electrical position of the rotor.

Ports

Input

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`V_α` — α-axis voltage
scalar

Voltage component along the α-axis in the stationary αβ reference frame.

Data Types: single | double | fixed point

`V_β` — β-axis voltage
scalar

Voltage component along the β-axis in the stationary αβ reference frame.

Data Types: single | double | fixed point

`I_α` — α-axis current
scalar

Current along the α-axis in the stationary αβ reference frame.

Data Types: single | double | fixed point

`I_β` — β-axis current
scalar

Current along the β-axis in the stationary αβ reference frame.

Data Types: single | double | fixed point

`Rst` — Reset block
scalar

The pulse (true value) that resets the block algorithm.

Data Types: single | double | fixed point

Output

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`θ_e` — Electrical position of PMSM
scalar

The electrical position of the rotor as estimated by the block.

Dependencies

To enable this port, set Block output to Position.

Data Types: single | double | fixed point

`Ψ` — Rotor flux of PMSM
scalar

The magnetic flux of the rotor as estimated by the block.

Dependencies

To enable this port, set Block output to Flux.

Data Types: single | double | fixed point

`T_e` — Electrical torque of PMSM
scalar

The electrical torque of the rotor as estimated by the block.

Dependencies

To enable this port, set Block output to Torque.

Data Types: single | double | fixed point

Parameters

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Motor parameters

`Input units` — Unit of voltage and current inputs
`SI unit` (default) | `Per-unit`

Select the unit of the α and β-axes voltage and current input values.

`Block output` — Select outputs that block should compute
`Position` (default) | `Flux` | `Torque`

Select one or more quantities that the block should compute and display in the block output.

Note

You must select at least one value. The block displays an error message if you click Ok or Apply without selecting any value.

`Pole pairs` — Number of pole pairs available in motor
`4` (default) | scalar

Number of pole pairs available in the motor.

Dependencies

To enable this parameter, set Block output to Torque.

`Stator resistance (ohm)` — Stator winding resistance
`0.36` (default) | scalar

Stator phase winding resistance of the motor in ohms.

`Stator d-axis inductance (H)` — Stator winding inductance along d-axis
`0.2e-3` (default) | scalar

Stator winding inductance of the motor along d-axis in Henry.

`Block sample time (S)` — Sample time after which block executes again
`50e-6` (default) | scalar

The fixed time interval in seconds between two consecutive instances of block execution.

Datatypes

`Position unit` — Unit of electrical position output
`Radians` (default) | `Degrees` | `Per-unit`

Unit of the electrical position output.

Dependencies

To enable this parameter, set Block output to Position.

`Position datatype` — Data type of electrical position output
`single` (default) | `double` | `fixed point`

Data type of the electrical position output.

Dependencies

To enable this parameter, set Block output to Position.

`Flux unit` — Unit of magnetic flux output
`Weber` (default) | `Per-unit`

Unit of the magnetic flux output.

Dependencies

To enable this parameter, set Block output to Flux.

`Flux datatype` — Data type of magnetic flux output
`single` (default) | `double` | `fixed point`

Data type of the magnetic flux output.

Dependencies

To enable this parameter, set Block output to Flux.

`Torque unit` — Unit of electrical torque output
`Nm` (default) | `Per-unit`

Unit of the electrical torque output.

Dependencies

To enable this parameter, set Block output to Torque.

`Torque datatype` — Data type of electrical torque output
`single` (default) | `double` | `fixed point`

Data type of the electrical torque output.

Dependencies

To enable this parameter, set Block output to Torque.

Model Examples

Sensorless Field-Oriented Control of PMSM

Implements the field-oriented control (FOC) technique to control the speed of a three-phase permanent magnet synchronous motor (PMSM). For details about FOC, see Field-Oriented Control (FOC).

References

[1] O. Sandre-Hernandez, J. J. Rangel-Magdaleno and R. Morales-Caporal, "Simulink-HDL cosimulation of direct torque control of a PM synchronous machine based FPGA," 2014 11th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Campeche, 2014, pp. 1-6. (doi: 10.1109/ICEEE.2014.6978298)

[2] Y. Inoue, S. Morimoto and M. Sanada, "Control method suitable for direct torque control based motor drive system satisfying voltage and current limitations," The 2010 International Power Electronics Conference - ECCE ASIA -, Sapporo, 2010, pp. 3000-3006. (doi: 10.1109/IPEC.2010.5543698)

Documentation

Flux Observer

Description

Equations

Ports

Input

Vα — α-axis voltage scalar

Vβ — β-axis voltage scalar

Iα — α-axis current scalar

Iβ — β-axis current scalar

Rst — Reset block scalar

Output

θe — Electrical position of PMSM scalar

Dependencies

Ψ — Rotor flux of PMSM scalar

Dependencies

Te — Electrical torque of PMSM scalar

Dependencies

Parameters

Motor parameters

Input units — Unit of voltage and current inputs SI unit (default) | Per-unit

Block output — Select outputs that block should compute Position (default) | Flux | Torque

Pole pairs — Number of pole pairs available in motor 4 (default) | scalar

Dependencies

Stator resistance (ohm) — Stator winding resistance 0.36 (default) | scalar

Stator d-axis inductance (H) — Stator winding inductance along d-axis 0.2e-3 (default) | scalar

Block sample time (S) — Sample time after which block executes again 50e-6 (default) | scalar

Datatypes

Position unit — Unit of electrical position output Radians (default) | Degrees | Per-unit

Dependencies

Position datatype — Data type of electrical position output single (default) | double | fixed point

Dependencies

Flux unit — Unit of magnetic flux output Weber (default) | Per-unit

Dependencies

Flux datatype — Data type of magnetic flux output single (default) | double | fixed point

Dependencies

Torque unit — Unit of electrical torque output Nm (default) | Per-unit

Dependencies

Torque datatype — Data type of electrical torque output single (default) | double | fixed point

Dependencies

Model Examples

Sensorless Field-Oriented Control of PMSM

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion Design and simulate fixed-point systems using Fixed-Point Designer™.

See Also

Motor Control Blockset Documentation

Support

`V_α` — α-axis voltage
scalar

`V_β` — β-axis voltage
scalar

`I_α` — α-axis current
scalar

`I_β` — β-axis current
scalar

`Rst` — Reset block
scalar

`θ_e` — Electrical position of PMSM
scalar

`Ψ` — Rotor flux of PMSM
scalar

`T_e` — Electrical torque of PMSM
scalar

`Input units` — Unit of voltage and current inputs
`SI unit` (default) | `Per-unit`

`Block output` — Select outputs that block should compute
`Position` (default) | `Flux` | `Torque`

`Pole pairs` — Number of pole pairs available in motor
`4` (default) | scalar

`Stator resistance (ohm)` — Stator winding resistance
`0.36` (default) | scalar

`Stator d-axis inductance (H)` — Stator winding inductance along d-axis
`0.2e-3` (default) | scalar

`Block sample time (S)` — Sample time after which block executes again
`50e-6` (default) | scalar

`Position unit` — Unit of electrical position output
`Radians` (default) | `Degrees` | `Per-unit`

`Position datatype` — Data type of electrical position output
`single` (default) | `double` | `fixed point`

`Flux unit` — Unit of magnetic flux output
`Weber` (default) | `Per-unit`

`Flux datatype` — Data type of magnetic flux output
`single` (default) | `double` | `fixed point`

`Torque unit` — Unit of electrical torque output
`Nm` (default) | `Per-unit`

`Torque datatype` — Data type of electrical torque output
`single` (default) | `double` | `fixed point`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.